Tracking the motion of objects is a common problem encountered in many fields. A variety of techniques have been used to determine the position of an object as that object moves through space.
Optical flow and its derivatives can be used to track the motion of an object. In optical flow, motion is calculated by comparing successive two-dimensional (referred to herein, alternatively, as “2-dimensional” or “2-D”) images. The images can either be acquired by a camera located on the object that is in motion or acquired by a camera that is viewing the scene in which the object in motion appears. In the first case, the pixel shift in the 2-dimensional images corresponds to the motion of the object. In the second case, the pixel shift of the object within the field of view of the 2-dimensional camera corresponds to the motion of the object. In either case, the translation of the object and the rotation of the object need to be inferred from the pixel shift. Because a conventional 2-dimensional image system projects all of the data in a scene onto a flat plane (the image sensor), calculation of the translation and rotation in three-dimensional (referred to herein, alternatively, as “3-dimensional” or “3-D”) space is difficult. It is known that this calculation can be improved by placing markers on the object in motion at known relative positions. Placing multiple spherical markers on the object in motion at known relative positions improves the ability to detect rotation of the object.